Related papers: Unified dynamical systems on coarse spaces

We study continuous 2-valued dynamical systems with discrete time (dynamics) on $\mathbb{C}$. The main question addressed is whether a 2-valued dynamics can be defined by the action of a 2-valued group. We construct a class of strongly…

Chronotaxic systems represent deterministic nonautonomous oscillatory systems which are capable of resisting continuous external perturbations while having a complex time-dependent dynamics. Until their recent introduction in \emph{Phys.…

An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the…

The term "hybrid system" refers to a continuous time dynamical system that undergoes Markovian perturbations at discrete time intervals. In this paper, we find that under the right formulation, a hybrid system can be treated as a dynamical…

Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…

Consider the macroscale modelling of microscale spatiotemporal dynamics. Here we develop a new approach to ensure coarse scale discrete models preserve important self-adjoint properties of the fine scale dynamics. The first part explores…

I briefly review some concepts related to coarse-graining methods for the dynamics of soft matter systems and argue that such schemes will almost always need to telescope down the physical hierarchy of time-scales to a more compressed, but…

A new class of deterministic dynamical systems, termed semipredictable dynamical systems, is presented. The spatiotemporal evolution of these systems have both predictable and unpredictable traits, as found in natural complex systems. We…

A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…

Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…

Periodic orbit theory provides two important functions---the dynamical zeta function and the spectral determinant for the calculation of dynamical averages in a nonlinear system. Their cycle expansions converge rapidly when the system is…

The period set of a dynamical system is defined as the subset of all integers $n$ such that the system has a periodic orbit of length $n$. Based on known results on the intersection of period sets of torus maps within a homotopy class, we…

We consider a class of dynamical systems, which we call weakly coarse expanding, which is a generalization to the postcritically infinite case of expanding Thurston maps as discussed by Bonk-Meyer and is closely related to coarse expanding…

This paper is concerned with the study of fuzzy dynamical systems. Let (X;M; *) be a fuzzy metric space in the sense of George and Veeramani. A fuzzy discrete dynamical system is given by any fuzzy continuous self-map defined on X. We…

We prove that generically and modulo a topological conjugacy there is only one dynamical system.

Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…

A machine learning technique is proposed for quantifying uncertainty in power system dynamics with spatiotemporally correlated stochastic forcing. We learn one-dimensional linear partial differential equations for the probability density…

We define the orbit morphism of partial dynamical systems and prove that an orbit morphism being an isomorphism in the category of partial dynamical systems and orbit morphisms is equivalent to the existence of a continuous orbit…

In this monograph we lay the foundation for a theory of coarse groups and coarse actions. Coarse groups are group objects in the category of coarse spaces, and can be thought of as sets with operations that satisfy the group axioms "up to…

Topological bases of behaviour of trajectories for autonomous differential systems of the second order on sphere are stated. Stereographic atlas of trajectories is constructed. Differential connections between trajectories of…